Answer: 60
Step-by-step explanation:
If the entire blue length is 100 and one of the parts of that is 64, the other part is 36.
So by the geometric mean theorem, letting the length of the dotted altitude be y,
[tex]\frac{64}{y}=\frac{y}{36}\\y^{2}=64 * 36 =2304\\y=48[/tex]
So if y=48, by the Pythagorean[tex]x=\sqrt{48^2 + 36^2}=60[/tex] theorem,
